This invention relates to a device for measuring rotational angles of a rotating shaft of a machine between a defined reference angle position of the shaft and an angle position at the instant of occurrence of a phenomenon caused by the function of the machine reference angle position being defined by a sign applied on the shaft, device comprising transducers, the signals of which are released by one or several reference angle signs or the machine characteristic phenomenon respectively, and being input to a processing unit which transforms the gate signal defined by the time interval between a reference angle signal and the machine characteristic signal into a signal proportional to the rotational angle.